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Abstract:\u00a0<\/strong>The Kochen-Specker (KS) theorem is often taken as a notion of nonclassicality that is independent of\u00a0entanglement since it is provable on a three-dimensional Hilbert space. However, the smallest system on which both\u00a0the KS theorem and entanglement are meaningful notions of nonclassicality is a two-qubit system. I will present some\u00a0recent work on the necessity of entanglement in proofs of the KS theorem on multiqubit systems. We show two key\u00a0results: firstly, that any proof of the KS theorem that uses KS sets necessarily requires entangled measurements, and\u00a0secondly, that a statistical proof of the KS theorem with unentangled measurements on a multiqubit state exists if and\u00a0only if this state can witness a Bell inequality violation. We also obtain an overall understanding of the relationship\u00a0between unentangled Gleason and KS theorems on multiqudit systems in general. Time permitting, I will also discuss\u00a0some implications of these results for the role of contextuality as a resource for multiqubit quantum computation with\u00a0state injection. <\/p><\/p>\n\n\n\n Based on arXiv:2109.13594.<\/p><\/p>\n\n\n\n When:<\/strong> 8th November, 2022<\/p>\n\n\n\n Where:<\/strong> Luminy, room 04.05 of building TPR2. CaNa seminar. <\/p>\n\n\n\n